Both of the right triangular prisms shown have bases that are right triangles with hypotenuse length 10 cm. One prism has height x and a base leg of length 6 cm. The other prism has height x - 2 cm and a base leg of length 5*sqrt(2) cm. The prism with height x - 2 cm has a volume that is 75% the volume of the prism of height x. What is the value of x?
+128406 First prism
Other leg length = sqrt (10^2 - 6^2) =sqrt (64) = 8
Volume of this prism = base area * height = (1/2) (6 * 8) * x = 24x
Second prism
Other leg length = sqrt (10^2 - 50) =sqrt (50)
Volume of this prism (1/2) (sqrt 50)^2 * ( x - 2 ) = 25 ( x - 2)
And we know that
.75 (24x) = 25 ( x - 2)
18x = 25x - 50 rearrange as
25x - 18x = 50
7x = 50
x = 50 / 7
